(3b^2c^-4/6b^-4c^-2)^-4

Question

 Im having trouble understanding all of the rules of the laws of exponents! 

Answer 1

When you have a negative exponent, you want to perform the reciprocal of the term that is associated with that exponent.  This will make the exponent positive.  In addition, in some cases, you will need to expand the term based on the value of the exponent. And when dividing terms with common bases, divide the coefficients and subtract the exponents.

 

Here is an example:

 

3x^-2 = 3 / x²

 

(3x)^-2 = 1 / (3x)² = 1 / (3x)(3x) = 1 / (9x²)

 

2b³ / 5b⁶ = (2/5)b^-3 = 2 / (5b³)

 

 

Apply this concept to the expression you posted here.

Answer 2

Very simple.  Exponents just repeats the value. Another words, they multiply themselves.

For example:

x² means x * x 

x³ means x * x * x

 

(x-1)² means (x-1)(x-1) equals x²-2x+1

(x-1)³ means (x-1)(x-1)(x-1) equals x³-3x²=3x-1

 

A negative exponent just means the reciprocal of the value.

x^-1 means 1/x

x^-2 means 1/x²

 

(x-1)^-1 means 1/(x-1)

(x-1)^-2 means 1/(x-1)² equals 1/((x-1)(x-1)) equals 1/(x²-2x+1)

 

 

For very simple terms.

3²=(3)(3)=9 and 3^-2=1/(3)(3)=1/9

NOT

(3)(2)=6 and (3)(-2)=-6

 

 

I hope this helps about exponents.

 

Answer 3

(3b²c^-4 / 6b^-4c^-2)^-4          reduce the integers

(b²c^-4 / 2b^-4c^-2)^-4                exponent of numerator minus exponent of denominator

(b⁶c^-2 / 2 )^-4                   power to power is product of powers

b^-24c^{8 /} 2                        convert negative exponent of positive

c⁸ / 2b²⁴